Benzene Dimer:  A Good Model for π−π Interactions in Proteins? A Comparison between the Benzene and the Toluene Dimers in the Gas Phase and in an Aqueous Solution

We have investigated the relative orientational preference of two benzene and two toluene molecules in a vacuum and in water, by means of free energy calculations. The gas-phase simulations reveal that, whereas the T-shaped benzene dimer is 0.78 kcal/mol lower in free energy than its stacked homologue, the sandwich arrangement of the toluene dimer is preferred over the T-shaped structure by 0.18 kcal/mol. MP2/TZP ab initio binding energies, evaluated for both dimers, were found to be consistent with the molecular mechanical estimates, hence suggesting that the van der Waals and the electrostatic contributions to the macromolecular force field employed herein are well balanced. We further note that our results agree quite nicely with the experimental binding energies of Neusser and Krause, obtained from breakdown measurements. The tendency witnessed in the gas phase is magnified in an aqueous solution, with differences in free energy between the T-shaped and the sandwich arrangements of the benzene and the toluene dimers equal to −1.47 and 1.12 kcal/mol, respectively. The calculated association constants and osmotic second virial coefficients also correlate reasonably well with the experimental data of Tucker and Christian. The conflict between the orientational preferences of the benzene and the toluene dimers is suggestive that trends in “π−π” interactions in proteins should be rationalized by other factors than simple electrostatic/dispersion considerations. The analysis of Phe−Phe pairs in protein crystallographic structures sheds light on the influence of both sterical hindrances and ancillary interactions between the aromatic moities and neighboring functional groups on the orientational preference of the phenyl rings.